Applications of (M,N)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions

Wanas, Abbas Kareem; Cotîrlǎ, Luminiţa-Ioana

doi:10.3390/math10040595

Cited by 15 publications

(8 citation statements)

References 55 publications

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“…There are some studies in the literature associated with the Fibonacci and Lucas polynomials, for example, see Refs. [4][5][6][7], among others.…”

Section: Respectivelymentioning

confidence: 99%

On Gaussian Leonardo Hybrid Polynomials

Yağmur

2023

Symmetry

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In the present paper, we first study the Gaussian Leonardo numbers and Gaussian Leonardo hybrid numbers. We give some new results for the Gaussian Leonardo numbers, including relations with the Gaussian Fibonacci and Gaussian Lucas numbers, and also give some new results for the Gaussian Leonardo hybrid numbers, including relations with the Gaussian Fibonacci and Gaussian Lucas hybrid numbers. For the proofs, we use the symmetric and antisymmetric properties of the Fibonacci and Lucas numbers. Then, we introduce the Gaussian Leonardo polynomials, which can be considered as a generalization of the Gaussian Leonardo numbers. After that, we introduce the Gaussian Leonardo hybrid polynomials, using the Gaussian Leonardo polynomials as coefficients instead of real numbers in hybrid numbers. Moreover, we obtain the recurrence relations, generating functions, Binet-like formulas, Vajda-like identities, Catalan-like identities, Cassini-like identities, and d’Ocagne-like identities for the Gaussian Leonardo polynomials and hybrid polynomials, respectively.

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“…There are some studies in the literature associated with the Fibonacci and Lucas polynomials, for example, see Refs. [4][5][6][7], among others.…”

Section: Respectivelymentioning

confidence: 99%

On Gaussian Leonardo Hybrid Polynomials

Yağmur

2023

Symmetry

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“…This functional has garnered significant attention, especially in the study of various subfamilies of univalent functions. Geometric function theory researchers are now actively exploring this subject [16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Applications of Horadam Polynomials for Bazilevič and λ-Pseudo-Starlike Bi-Univalent Functions Associated with Sakaguchi Type Functions

Al-Shbeil,

Wanas,

AlAqad

et al. 2024

Symmetry

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In this study, we introduce a new class of normalized analytic and bi-univalent functions denoted by DΣ(δ,η,λ,t,r). These functions are connected to the Bazilevič functions and the λ-pseudo-starlike functions. We employ Sakaguchi Type Functions and Horadam polynomials in our survey. We establish the Fekete-Szegö inequality for the functions in DΣ(δ,η,λ,t,r) and derive upper bounds for the initial Taylor–Maclaurin coefficients |a2| and |a3|. Additionally, we establish connections between our results and previous research papers on this topic.

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“…Many works on the bi-univalent functions have been presented in the previous papers (see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). We recall some examples of functions in the family Σ, from the work of Srivastava et al [21],…”

Section: Introductionmentioning

confidence: 99%

On a Fekete–Szegö Problem Associated with Generalized Telephone Numbers

et al. 2023

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One of the important problems regarding coefficients of analytical functions (i.e., Fekete–Szegö inequality) was raised by Fekete and Szegö in 1933. The results of this research are dedicated to determine upper coefficient estimates and the Fekete–Szegö problem in the class WΣ(δ,λ;ϑ), which is defined by generalized telephone numbers. We also indicate some specific conditions and consequences of results found by us.

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Applications of (M,N)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions

Cited by 15 publications

References 55 publications

On Gaussian Leonardo Hybrid Polynomials

On Gaussian Leonardo Hybrid Polynomials

Applications of Horadam Polynomials for Bazilevič and λ-Pseudo-Starlike Bi-Univalent Functions Associated with Sakaguchi Type Functions

On a Fekete–Szegö Problem Associated with Generalized Telephone Numbers

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